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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 6, pp 967–1004 | Cite as

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

  • Gui-Qiang G. ChenEmail author
  • Peter H. C. PangEmail author
Article
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Abstract

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises. Some further developments, problems, and challenges in this direction are also discussed.

Keywords

Stochastic solutions Entropy solutions Invariant measures Existence Uniqueness Stochastic forcing Anisotropic degenerate Parabolichyperbolic equations Long-time behavior 

2000 MR Subject Classification

35B40 35K65 37-02 37A50 37C40 60H15 35Q35 58J70 60G51 60J65 

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Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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